Group chase and escape in the presence of obstacles
Abstract We study a stochastic lattice model describing the dynamics of a group chasing and escaping between two species in an environment that contains obstacles. The Monte Carlo simulations are carried out on a two-dimensional square lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. The model includes smart pursuit (chasers to targets) and evasion (targets from chasers). Both species can affect their movement by visual perception within their finite sighting range σ . We concentrate here on the role that density and shape of the obstacles plays in the time evolution of the number of targets, N T ( t ) . Temporal evolution of the number of targets N T ( t ) is found to be stretched-exponential, of the form N T ( t ) = N T ( 0 ) − δ N T ( ∞ ) 1 − exp [ − ( t ∕ τ ) β ] , regardless of whether the obstacles are present or not. The characteristic timescale τ is found to decrease with the initial density of targets ρ 0 T according to a power-law, i.e., τ ∝ ( ρ 0 T ) − γ . Furthermore, temporal dependences of the number of targets N T ( t ) are compared for various combinations of chasers and targets with different sighting ranges, σ = 1 , 2 , in order to analyze the relationship between the ability of species and the capture dynamics in the presence of obstacles.